The home side started brightly at the Strathclyde Homes Stadium, with Bryan Prunty and Phillip Johnston both seeing efforts saved by Accies keeper Kevin Cuthbert.
But Hamilton went ahead in the 21st minute when Ali Crawford's low 20-yard drive beat the despairing dive of home keeper Stephen Grindlay.
The hosts were level on 34 thanks to an own goal from Lee Kilday who turned James Lister's flick on from Mark Lamont's centre into his own net.
Lister saw a header rebound off the post before putting the Sons 2-1 up on 73 when he nodded in Lamont's left-wing cross.
Prunty then looked to have sealed the win for Dumbarton four minutes later as he tapped home after Lamont's shot was parried by Cuthbert.
Substitute James Keatings gave Hamilton hope when he pulled a goal back with two minutes remaining from Stevie May's centre and he then grabbed an equaliser deep into injury-time to break home hearts.